    
Before showing the mentioned no-go results we like to study \(\mathcal {M}\)  in some detail. Many examples at the level of exercises serve to become more familiar with
\(\mathcal {M}\)  and can be skipped. Only (REF ) is needed in the sequel. In particular it shows that there are maximal spacelike sets, which are not bases. In (REF ) it will be proven that causally complete sets are automatically measurable, i.e., Lebesgue measurable subsets of \(\mathbb {R}^4\) . Regarding the definition of \(\mathcal {M}\)  we follow [1]}.

